【摘要】 <正> 我们知道算子半群是求解微分方程的一个工具[4]、[5]、[6]。设(?)是Hilbert空间,A是(?)的线性算子,其定义域为(?)(A),考虑非齐次的发展型方程 u′(t)+Au(t)=f(t) 其中f(t)是[0,∞)→(?)的抽象函数,当t∈[0,∞)时,f(t)∈(?)。所谓Cauchy问题就是求一个[0,∞)→(?)的抽象函数u(t),使得u在[0,∞)上有连续的导数,即u∈C′([0,∞),(?)),当更多还原

【Abstract】 In this paper we generalized the relationship between generators of unitary groups and self-adjoint differential operators to generators of contraction strongly continuous semigroups and some non-self-adjoint differential operators. We found a limit-point criterion for a class of 2Nth-ordor non-self-adjoint ordinary differential operators. The main result is the following theorem: Let be an regular ordinary differential expression on [a,∞], each pk（x）≥0 is a C^∞ function and pN（x） is non-vanishing, M is an operator with real coefficients and M=M⁺, order≤2N, suppose that H is the restriction of the maximal operator T₁（L） to the set Then L is limit-point, if and only if H is the generator of a contraction strongly continuous semigroups.更多还原